Solve for x log base x of 81=4

Problem

(log_x)(81)=4

Solution

1. Rewrite the logarithmic equation in its equivalent exponential form using the definition (log_b)(a)=c⇔bc=a

x4=81

2. Express the constant 81 as a power with an exponent of 4 to match the left side of the equation.

x4=3

3. Solve for x by taking the fourth root of both sides.

x=√(4,81)

4. Simplify the root, noting that the base of a logarithm must be positive and not equal to 1.

x=3

Final Answer

(log_x)(81)=4⇒x=3

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